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What are these bubbles? What reaction is taking place?

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Magnesium often forms bubbles in metal displacement reactions such as this one. See, for instance, this answer where a similar phenomenon is seen with copper as the displaced metal.

Magnesium reacts with liquid water to generate hydrogen, but only slowly when the water is pure due to the low solubility of the hydroxide that is also formed in this reaction ($\ce{Mg + 2H2O -> Mg(OH)2 + H2}$). But even a slightly acidic solution, such as that usually formed when a transition or post-transition metal salt is dissolved in water, dissolves the hydroxide and the hydrogen displacement then becomes faster and more noticeable.

For an introductory experiment, zinc would make a better reducing metal, displacing copper, or we can use the classic iron nail in a copper salt solution. These choices avoid the hydrogen displacement side reaction, and we see the metal displacement reaction more cleanly.

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